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Hopf–Rinow theorem
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==References== {{refbegin}} * {{wikicite|ref={{sfnRef|Burago|Burago|Ivanov|2001}}|reference={{cite book|mr=1835418|zbl=0981.51016|last1=Burago|first1=Dmitri|last2=Burago|first2=Yuri|last3=Ivanov|first3=Sergei|title=A course in metric geometry|series=[[Graduate Studies in Mathematics]]|volume=33|publisher=[[American Mathematical Society]]|location=Providence, RI|year=2001|isbn=0-8218-2129-6|author-link1=Dmitri Burago|author-link2=Yuri Burago|author-link3=Sergei Ivanov (mathematician)|doi=10.1090/gsm/033|ref=none}} {{erratum|https://www.pdmi.ras.ru/~svivanov/papers/bbi-errata.pdf|checked=yes}}}} * {{cite book|mr=1744486|last1=Bridson|first1=Martin R.|last2=Haefliger|first2=André|title=Metric spaces of non-positive curvature|series=Grundlehren der mathematischen Wissenschaften|volume=319|publisher=[[Springer-Verlag]]|location=Berlin|year=1999|isbn=3-540-64324-9|doi=10.1007/978-3-662-12494-9|author-link1=Martin Bridson|author-link2=André Haefliger|zbl=0988.53001}} * {{cite book|last=do Carmo|first=Manfredo Perdigão|authorlink=Manfredo do Carmo|title=Riemannian geometry|series= Mathematics: Theory & Applications|year=1992|isbn=0-8176-3490-8|location=Boston, MA|publisher=[[Birkhäuser|Birkhäuser Boston, Inc.]]|others=Translated from the second Portuguese edition by Francis Flaherty|zbl=0752.53001|mr=1138207}} * {{cite book|last1=Gallot|first1=Sylvestre|author-link1=Sylvestre Gallot|last2=Hulin|first2=Dominique|author-link2=Dominique Hulin|last3=Lafontaine|first3=Jacques|title=Riemannian geometry|year=2004|edition=Third|series=Universitext|publisher=[[Springer-Verlag]]|mr=2088027|isbn=3-540-20493-8|doi=10.1007/978-3-642-18855-8|zbl=1068.53001}} * {{cite book|last1=Gromov|first1=Misha|title-link=Metric Structures for Riemannian and Non-Riemannian Spaces|title=Metric structures for Riemannian and non-Riemannian spaces|edition=Based on the 1981 French original|series=Progress in Mathematics|volume=152|publisher=[[Birkhäuser|Birkhäuser Boston, Inc.]]|location=Boston, MA|year=1999|isbn=0-8176-3898-9|mr=1699320|translator-last1=Bates|translator-first1=Sean Michael|others=With appendices by [[Mikhail Katz|M. Katz]], [[Pierre Pansu|P. Pansu]], and [[Stephen Semmes|S. Semmes]].|doi=10.1007/978-0-8176-4583-0|zbl=0953.53002|author-link1=Mikhael Gromov (mathematician)}} * {{cite book|last1=Jost|first1=Jürgen|title=Riemannian geometry and geometric analysis|series=Universitext|author-link1=Jürgen Jost|edition=Seventh edition of 1995 original|publisher=[[Springer, Cham]]|year=2017|isbn=978-3-319-61859-3|mr=3726907|doi=10.1007/978-3-319-61860-9|zbl=1380.53001}} * {{cite book|author-link1=Shoshichi Kobayashi|author-link2=Katsumi Nomizu|last1=Kobayashi|first1=Shoshichi|last2=Nomizu|title-link=Foundations of Differential Geometry|first2=Katsumi|title=Foundations of differential geometry. Volume I |publisher=[[John Wiley & Sons, Inc.]]|location=New York–London|year=1963|mr=0152974|zbl=0119.37502}} * {{cite book|mr=1666820|last1=Lang|first1=Serge|title=Fundamentals of differential geometry|series=[[Graduate Texts in Mathematics]]|volume=191|publisher=[[Springer-Verlag]]|location=New York|year=1999|isbn=0-387-98593-X|doi=10.1007/978-1-4612-0541-8|author-link1=Serge Lang|zbl=0932.53001}} * {{cite book|last1=O'Neill|first1=Barrett|author-link1=Barrett O'Neill|title=Semi-Riemannian geometry. With applications to relativity|series=Pure and Applied Mathematics|volume=103|publisher=[[Academic Press|Academic Press, Inc.]]|location=New York|year=1983|isbn=0-12-526740-1|mr=0719023|zbl=0531.53051|doi=10.1016/s0079-8169(08)x6002-7}} * {{cite book|last1=Petersen|first1=Peter|title=Riemannian geometry|edition=Third edition of 1998 original|series=[[Graduate Texts in Mathematics]]|volume=171|publisher=[[Springer Publishing|Springer, Cham]]|year=2016|isbn=978-3-319-26652-7|mr=3469435|doi=10.1007/978-3-319-26654-1|zbl=1417.53001}} {{refend}}
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